Single-ended fluorescent lamps, for example of the type described in the referenced patent, U.S. Pat. No. 4,481,442, Albrecht et al., or U.S. Pat. No. 4,374,340 have end portions at the discharge vessels formed by press or pinch seals which end portions extend into the interior of a hollow base. The base and the fluorescent tubes are connected by a cement which hardens when heated. The fixed connection between the lamp and the base will occur only after the temperature has acted on the cement, as well as on the glass elements of the discharge vessel for some time. In mass-production of such lamps, the basing machine thus has to supply continuously for some periods of time the heat necessary to harden the connecting cement. This is expensive and time-consuming and interferes with high-speed manufacture. The use of base constructions, that are entirely made of plastic material, was greatly narrowed since the connecting base cement requires a certain minimum temperature for hardening, which is not readily compatible with the maximum temperature that most plastic base materials can accept without deformation or damage thereto.